Public transport applications, which aim to propose the ideal route to end users, have commonly been used by passengers. However, the ideal route for public transport varies depending on the preferences of users. The shortest path is preferred by most users as a primary criterion for the ideal route. According to our research, Dijkstra's Algorithm is mostly used in order to find shortest path. However, Dijkstra's Algorithm is not efficient for public transport route planning, because it ignores number of transfers and walking distances. Thus, in order to minimize these shortcomings, Dijkstra's Algorithm is modified by implementing penalty system in our study. Additionally, our modified algorithm is tested on the real world transport network of Izmir and compared with the results of Dijkstra's Algorithm. It is observed that our modified algorithm is quite efficient for route planning in the public transport network in terms of the number of transfers, distance of proposed route and walking distance.